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## THE CALCULATION OF CURRENT OF MAINTAINING FIELD IN TOROIDAL PLASMA EQUILIBRIUM

ZHANG CHUN-YUAN, SUN JI-GUANG, QING CHENG-RUI
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• #### 摘要

本文介绍一个计算轴对称任意截面环形等离子体平衡问题的方法。先选定等离子体边界和环电流分布,用有限元方法解平衡方程的边值问题。借助于虚壳原理,得到用平衡方程解表示的能够产生平衡时所需要的维持场的虚壳电流。计算虚壳电流在等离子体区的维持场,以它为根据,采用积分方程开拓,求等离子体区外某位形上的维持场电流分布。解决这个问题的主要困难是当磁场向外开拓时遇到了不适定问题。我们用奇异值分解方法解不适定的Fredholm第一类积分方程。这个方法能容易地找到稳定解,对解决这个平衡问题是简单有效的。我们以七种等离子体截面形状,三种电流分布为具体模型,在三种维持场电流分布位形上给出了维持场电流分布。还给出了维持场形态,维持场总电流与等离子体总电流的比较,并简单讨论了维持场对等离子体整体稳定性的影响。

#### Abstract

In this paper a method is presented for solving the equilibrium problem with axisymmetry for arbitraryly given plasma configurations. First, the boundary value problem of equilibrium equation is solved by finite element method for a given plasma boundary and current distribution. Then, based on virtual-casing principle, the virtual-casing current which produces the maintaining magnetic field requisite for the equilibrium is obtained by using solution of the equilibrium equation. The field of virtual-casing current, i.e. the maintaining field inside plasma is calculated. The current distribution of maintaining field on a certain contour outside the plasma is found by means of solving the integral equation. The main difficulty confronted in solving the integral equation problem is that one has to deal with an incorrectly posed problem. We have solved the incorrectly posed Fredholm integral equation of first kind, using a method of singular value decomposition. This method is simple and effective in solving such an equilibrium problem.We have considered seven types of plasma configuration including circular, elliptic, doublet, race-track, D-, back D- and banana shapes and three kinds of plasma current distribution including quasi-uniform, diffusion-type and skin-type distribution. Three type of current distribution for maintaining field are obtained in a given circular-, elliptic- and -shapes. For the models as mentioned above, the current distribution of maintaining field and the field itself are given. The total currents of maintaining field and total plasma currents are compared with each other. Some influences of the maintaining fields on stability is discussed.

#### 参考文献

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##### 出版历程
• 收稿日期:  1979-07-23
• 刊出日期:  2005-07-29

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